You’re a big-time athlete, and you’re hurt. You can tell somebody about it and focus on getting healthy, or you can keep it to yourself and play through it.

What do you do?

Keep it to yourself. Then you’re Alex Rodriguez, and everybody is convinced you’re back to being a choker, and a washed-up, broken-down, overpaid one at that.

While he was in the middle of his playoff nightmare with the Yankees in October, he knew something was wrong. He mentioned it to someone, he was sent to be examined, he more or less checked out all right, he never mentioned it again, and his hitting nightmare resumed.

A-Rod was a national punch line by the time the Yankees were eliminated. Two months later, we find that he needs major hip surgery that will keep him out for as much as half of next season. Few, if any, apologies or retractions from his universe of critics have been forthcoming.

In that case …

Tell somebody. Then you’re Alex Smith or Michael Vick.

Smith suffered a concussion three weeks ago and had to be replaced as the 49ers starting quarterback the following week. Colin Kaepernick shredded the Chicago Bears. Kaepernick was named the starter for the following week – with head coach Jim Harbaugh specifying that it had nothing to do with Smith’s readiness to play. Smith, now apparently fully recovered, hasn’t played since.

Vick’s poor season with the Eagles, meanwhile, was interrupted by a concussion the same week Smith suffered his concussion. His replacement, Nick Foles, has lost each of his three starts since. On Monday, Foles was named the starter for the season’s final four games, regardless of if, or when, Vick is ready to play again.

So …

Sorry, big-time athlete. It was a trick question. You were offered a choice back there, but in reality, there is no choice. You’re damned if you do and damned if you don’t.

Unless you believe this to be a viable option, don’t get hurt at all, ever.

Right. Sound advice for, respectively, a 37-year-old third baseman with one hip operation in his past already, and a pair of NFL quarterbacks.

Forget that for a moment, though. What is the value of coming clean about an injury, weighed against keeping shut about it?

Not pushing the issue, either within the Yankees or publicly, appears to have done Rodriguez no good. Of course, he’s the captain of the lifetime Can’t-Win team, and he’s earned it.

But consider his alternatives. In the middle of a wretched slump even by his postseason standards, he could have made it clear that he was playing in serious pain and needed to sit down … or that he was in pain, but was going to try to grit his way through for the team.

It would have been a no-win situation for him. No credit for sacrificing himself for the good of the club. None for fighting through the pain and helping any way he could because he might be better at 50 percent than his replacements at 100 percent. None of that is the narrative of his career. One way or the other, the blame for the Yankees’ sputtering finish lands on him.

And while A-Rod is unique in that way, it’s not a unique reaction to injury in the bottom-line world of sports. There are shades of difference in perception between well-liked players and disliked ones, but in the end, if you’re injured, you’re not helping, and your team will act accordingly.

Ask Peyton Manning, once upon a time of the Indianapolis Colts. It’s safe to say he’s got a more forgiving base of public support than A-Rod. Lot of good it did him in the only NFL home he’d ever had.

Of course, some injuries can’t be hidden. Concussions are now at the top of the list. To its credit, the NFL is on a head trauma-prevention crusade, and its entire concussion protocol, from testing in-game to baseline testing afterwards, takes that critical decision out of the player’s hands. No more “Three fingers, Cincinnati, I feel fine, send me back in,’’ as it was for so many years.

But if there ever was a time that you could understand why players would hide any injuries if they could, it’s now.

In that atmosphere, here is Smith, who took his team to the NFC title game last season, saying plaintively as his fate is decided, “I feel like the only thing I did to lose my job was get a concussion.”

Meanwhile, Eagles coach Andy Reid claimed that Vick “was on board” with the decision. Gotta take his word for it. Vick is still recovering. He might not recover in the last four weeks of the season, and he might recover this week.

Doesn’t matter. His job belongs to someone else now.

The changes with Smith and Vick might have been inevitable anyway. Getting injured made them very convenient, though. If they hadn’t been hurt, things might be different … or if they had been able to hide being injured.

Now, though, neither has a chance to start again – unless the new starters get injured. So, if you’re Kaepernick or Foles, knowing exactly how you got your jobs, and you get hurt, and there’s a chance your coaches wouldn’t find out ...